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Author Topic: Resistor Network Brain teaser
Ti
Assimilated
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Icon 5 posted March 06, 2006 19:55      Profile for Ti   Author's Homepage     Send New Private Message       Edit/Delete Post   Reply With Quote 
Okay, so I sort of stumped myself. I was making resistor network diagrams for people to solve (You know da kine, that you have to solve for Rt given a bunch of series and parallel resistors), and the students were given the basic equations (Series = R1 + R2 ... Parallel = (R1^-1 + R2^-1)^-1), but there was one I devised that couldn't be solved with just those equations. I've removed all the flak, and this is what the basic catch boils down to:

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I've come up with a couple of possible equations for the solution to this sort of network, but through my research can't find a clear this is the right answer for sure answer. All call physicists?

Kevin

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Check out my webpage/blog/review stash
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Posts: 377 | From: Sunnyvale, CA | Registered: Oct 2001  |  IP: Logged
Cap'n Vic

Member # 1477

Icon 1 posted March 07, 2006 11:11      Profile for Cap'n Vic     Send New Private Message       Edit/Delete Post   Reply With Quote 
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Whoa! I haven’t had to exercise the old Ohm’s/Kirchoff’s law grey matter in quite a long time. This is like the M.C. Escher of circuits, I had to redraw it but it is still confusing as hell how R4 and R5 play into things.

Assume all values are 100Ω

In my drawing, R2 is in series with R5 and R4 are in parallel, the middle branch.

Middle branch:
R2 + (R5 + R2)/2
100 + (100+100)/2 = 200Ω

Left (R3) and Right (R1) branches are 100Ω each. They are in parallel with the middle branch:

R3 + R1 + middle branch/3
100 + 100 + 200/3 = 133.333Ω

133.3Ω For the big ‘W’

R6 and R7 are in parallel

R6 + R7/2
100 + 100/2 = 100Ω

Soooooooooo, 133.333Ω for the Big ‘W’ + 100Ω for the bottom section equals 233.333Ω

Posts: 5471 | From: One of the drones from sector 7G | Registered: Jun 2002  |  IP: Logged
N9IWP
Geek
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Icon 1 posted March 07, 2006 12:08      Profile for N9IWP     Send New Private Message       Edit/Delete Post   Reply With Quote 
One can use delta - y conversions
http://www.play-hookey.com/dc_theory/deriving_delta_y_conversions.html

A better technique is to use node analysis:
http://mysite.wanadoo-members.co.uk/phil_robinson/node.html

But it has been too many years for me to rememebr the details.

Posts: 181 | From: Southeast MN | Registered: Mar 2002  |  IP: Logged
quantumfluff
BlabberMouth, a Blabber Odyssey
Member # 450

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Icon 1 posted March 07, 2006 19:09      Profile for quantumfluff     Send New Private Message       Edit/Delete Post   Reply With Quote 
The node-analysis stuff is cool. I have not done resister networks since 1978 (back in high school) and they tried to teach physics without martix math back then.
Posts: 2901 | From: 5 to 15 meters above sea level | Registered: Jun 2000  |  IP: Logged


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